Want to prove Var(xy)=E[x]^2*var(y)+E[y]^2*var(x)+var(x)*var(y)

yabi

New member
Joined
Apr 19, 2021
Messages
1
Want to prove Var(xy)=E[x]^2*var(y)+E[y]^2*var(x)+var(x)*var(y)

I want to prove above-mentioned formula using following formula:
Var(y)=Ex[var(y/x)]+varx[E(y/x)]

In next step I want to prove the title-mentioned formula using Taylor series expansion.

Will be happy if someone could give a hint on how can I prove this formula.
 
Last edited by a moderator:

Subhotosh Khan

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
24,311
I want to prove above-mentioned formula using following formula:
Var(y)=Ex[var(y/x)]+varx[E(y/x)]

In next step I want to prove the title-mentioned formula using Taylor series expansion.
Can you provide mathematical equations to describe E(x) and var(x)

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem
 
Top